Filtering for a class of nonlinear MIMO uncertain time-delay stochastic systems

Abstract

In this article, a high-gain nonlinear observer-based approach is proposed for filtering of nonlinear stochastic systems with time delays. The system under consideration contains parameter uncertainties, stochastic disturbances, time delays, as well as Lipschitz-like nonlinearities. The objective is to design a robust filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in a sense of mean square. A new high-gain filter idea is introduced to solve the stochastic filtering problem by using the Lyapunov method and stochastic analysis techniques. The design of the proposed filter does not necessitate the resolution of any dynamics systems and its expression is explicitly given, i.e. its calibration is achieved through the choice of a single parameter, and does not rely on solving any matrix inequalities by numerical computation. A simulation example is given to illustrate the performance of the proposed filter.

Keywords:

• nonlinear system
• stochastic system
• MIMO system
• uncertain system
• exponential filtering
• time delay

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Acknowledgements

This work was supported in part by the Funds for Creative Research Groups of China (No. 60821063), the State Key Program of National Natural Science of China (Grant No. 60534010), National 973 Program of China (Grant No. 2009CB320604), the Funds of National Natural Science of China (Grant No. 60674021), the III Project (B08015) and the Funds of PhD program of MOE, China (Grant No. 20060145019).